Multimode Rayleigh wave inversion for heterogeneity and
azimuthal anisotropy of the Australian upper mantle

Frederik J Simons1, Rob D. van der Hilst1, Jean-Paul Montagner2, and Alet Zielhuis1

1 Department of Earth, Atmospheric and Planetary Sciences
Massachusetts Institute of Technology (MIT)
Cambridge MA 02139, USA

2 Laboratoire de Sismologie
Institut de Physique du Globe Paris (IPGP)
F-75005 Paris, France

Geophysical Journal International, 2002, 151 (3), 738-754, doi:10.1046/j.1365-246X.2002.01787.x

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We present an azimuthally anisotropic three-dimensional shear-wave speed model for the Australian upper mantle obtained from the dispersion of fundamental and higher modes of Rayleigh waves. We compare two tomographic techniques to map path-average Earth models into a 3-D model for heterogeneity and azimuthal anisotropy. Method I uses a rectangular surface cell parameterization and depth basis functions that represent independently constrained estimates of radial Earth structure. It performs an iterative inversion norm damping and gradient regularization. Method II uses a direct inversion of individual depth layers constrained by Bayesian assumptions about the model covariance. We recall that Bayesian inversions and discrete regularization approaches are theoretically equivalent, and with a synthetic example we show that they can give similar results. The model we present here uses the discrete regularized inversion of independent path constraints of Method I, on an equal-area grid. With the exception of westernmost Australia, we can retrieve structure on length scales of about 250 km laterally and 50 km in the radial direction, to within 0.8% for the velocity, 20% for the anisotropic magnitude and 20 degrees for its direction. On length scales of 1000 km and longer, down to about 200 km, there is a good correlation between velocity heterogeneity and geologic age. At shorter length scales and at depths below 200 km, however, this relationship breaks down. The observed magnitude and direction of maximum anisotropy do not, in general, appear to be correlated to surface geology. The pattern of anisotropy appears to be rather complex in the upper 150 km, whereas a smoother pattern of fast axes is obtained at larger depth. If some of the deeper directions of anisotropy are aligned with the approximately N--S direction of absolute plate motion, this correspondence is not everywhere obvious, despite the fast (7 cm/yr) northward motion of the Australian plate. This suggests that other mechanisms are important in creating the deeper anisotropy. Predictions of SKS splitting times and directions, an integrated measure of anisotropy, are poorly matched by observations of shear-wave birefringence.


  1. Figure 01 Distribution of stations and events used in this study.
  2. Figure 02 Equal-area, irregular, and tectonic grids used in the inversion.
  3. Figure 03 Synthetic test with uniform path coverage: input.
  4. Figure 04 Synthetic test with uniform path coverage: recovery with Bayesian and regularization techniques.
  5. Figure 05 Exact resolution computation for synthetic and real data sets.
  6. Figure 06 Checkerboard test with azimuthal anisotropy..
  7. Figure 07 Checkerboard input/output test at different depths.
  8. Figure 08 Trade-off of heterogeneity and anisotropy at 140 km.
  9. Figure 09 Inversion results at different depths.
  10. Figure 10 Inversion results at different depths: cross-sections
  11. Figure 11 Regionalized presentation of heterogeneity and anisotropy
  12. Figure 12 Predictions and observations of shear-wave splitting.

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